Modeling and control of cadmium zinc telluride grown via an electro-dynamic gradient freeze furnace.

Abstract

In this thesis, numerical models are used to study the effect of novel processing methods to grow bulk, single crystal cadmium zinc telluride (CZT) in a vertical Bridgman (VB) furnace. Additionally, we investigate new mathematical algorithms for improved solving capability of equations that describe such crystal growth systems.

A two-dimensional crystal growth model for the simulation of bulk crystal growth in a VB system is presented. This model consists of conservation equations for coupled continuum level transport of heat, mass, and momentum. Thermodynamic relations associated with phase change are also included. The Galerkin finite element method is used to discretize the spatial portion of the governing equations. The resulting sets of nonlinear algebraic equations are solved using Newton's method.

Novel processing methods that are not practical to attempt in experiments are investigated using numerical modeling. A two-dimensional, planar, crystal growth model is used to explore the effect of ampoule tilting on zinc segregation in a CZT crystal. Tilting is shown to improve lateral segregation. We also analyze the use of closed-loop control to improve the macroscopic melt-crystal interface shape during growth by changing the furnace temperature gradient. Targeted closed-loop control on the temperature gradient adjacent to the solid only gave the best results and unexpectedly produced a favorable convex shape.

A multi-scale crystal growth model is developed by coupling pre-existing codes, one which specializes in modeling the complex crystal growth process and the other which specializes in modeling the heat transfer effects in a furnace. Previously, a coupling algorithm based on the Gauss-Seidel method was used but it converged unreliably [136, 196]. Here, we use an Approximate Block Newton approach where we approximate Newton's method used to solve the two separate models as if they were one monolithic model.

A Schur complement formulation is employed to solve the free-boundary problem associated with melt crystal growth systems. With this form, the difficult interface location part of the problem is mapped away from the equations governing transport. We assess the behavior of this method using two-dimensional simulations, but the goal is to improve solvability of three-dimensional problems.